Place the potatoes in a large saucepan and add water to just cover. Add the sea salt, cover and bring to a boil. Reduce the flame to medium and cook until done, about 20 to 25 minutes. Test with a fork periodically to check if they are tender. Remove, drain and cover with cold water. Let sit until the potatoes are cool enough to handle.
Cut the potatoes into chunks and place in a mixing bowl. Add the celery, onions, mustard, tofu mayonnaise and parsley. Gently mix until the potatoes are evenly coated with mayonnaise and mustard. Place in a serving dish and sprinkle the paprika over. Refrigerate until chilled, about 1 hour.
Per serving - 258 calories, 15 g fat (50% calories from fat), 4 g protein, 29 g carbohydrate, 3 g fiber, 0 mg cholesterol, 283 mg sodium